1. Multicarrier Modulations
1.1 OFDM Modulations
OFDM (Orthogonal Frequency Divisional Multiplex) type multicarrier modulations are known today. A modulation technique of this kind brings an efficient solution to the problem of the broadcasting information, especially for wired or wireless multiple-path channels.
Consequently, the OFDM multicarrier modulation technique has been chosen in several standards and specifications for applications in wired transmission, for example ADSL (Asymmetric Digital Subscriber Line) or PLC (Power Line Communication) or wireless transmission applications, for example systems of the DAB (Digital Audio Broadcasting), DVB-T (Digital Video Broadcasting-Terrestrial) or WLAN (Wireless Local Area Network) type.
However, the rectangular shaping of a signal made by an OFDM modulator has the drawback of poor frequency location.
Consequently, alternative solutions have been proposed, leading to the creation of multicarrier modulation systems in which the signal is shaped by functions known as prototype functions, enabling better frequency location to be obtained.
Indeed, the set of carriers of a multicarrier modulation forms a multiplex and each of the carriers of this multiplex can be shaped by means of a same prototype function, referenced g(t), which characterizes the multicarrier modulation.
1.2 OFDM/OQAM Modulations
Thus, one solution proposed consists in replacing a QAM (Quadrature Amplitude Modulation) implemented on each of the carriers by a modulation which offsets the real and imaginary parts of the complex symbols to be transmitted by a half symbol time, for two successive carrier frequencies.
This alternation leads to an OFDM/OQAM type multicarrier modulation. This approach makes it possible especially to obtain the desired conditions of orthogonality with prototype filters that are not necessarily rectangular in shape.
Indeed, the temporal offset introduced by OQAM modulation relaxes the constraints of orthogonality and more generally those of biorthogonality. This class of modulation thus offers a wider choice of prototype functions than the simple rectangular prototype function of an OFDM modulation.
Thus, depending on the type of transmission channel considered for a given application, for example the radiomobile or powerline communication (PLC) channel, it is possible to choose prototype functions appropriate to the types of distortion encountered. In particular, it is preferable to choose prototype functions showing higher frequency selectivity than the cardinal sine used in OFDM modulation, especially in radiomobile channels, to overcome the frequency dispersion due to the Doppler effect or in a PLC channel to withstand narrow-band noise phenomena with greater efficiency and generally to meet the frequency specifications of transmission masks with greater ease.
OFDM/OQAM modulation is therefore an alternative to classic OFDM modulation, relying on a judicious choice of the prototype function modulating each of the carriers of the signal which need to be well located in the time/frequency space.
In particular, FIG. 1 illustrates a time/frequency representation of the real-value data elements transmitted by OFDM/OQAM modulation and of the complex-value data elements transmitted by classic OFDM modulation without any guard interval, an OFDM/QAM complex value symbol or OFDM/OQAM real value symbol being formed by a set of data elements at a given point in time t. Furthermore, each time/frequency location bears a carrier frequency, called a sub-carrier or directly a carrier here below in the description.
In this FIG. 1, the triangles at a given point in time t represent the complex-value data elements of an OFDM/QAM symbol. The circles and asterisks shown at a given point in time t for their part represent the real-value data elements of an OFDM/OQAM symbol. For example, for two successive real-value OFDM/OQAM symbols, the circles correspond to the real part and the asterisks to the imaginary part of a complex symbol coming from a QAM constellation which it is sought to transmit by using an OFDM/OQAM modulation.
Indeed, for a complex type of classic OFDM modulation, the real and imaginary parts of a complex value coming from the QAM constellation are transmitted simultaneously, at intervals of every symbol time period Tu; however, in a real type of OFDM/OQAM modulation, the real and imaginary parts are transmitted with a temporal offset of one complex half symbol time (Tu/2).
It can be seen in FIG. 1 that the spectral efficiency of the OFDM/OQAM is identical to that of classic OFDM without any guard interval. Indeed, if ν0 denotes the spacing between two adjacent carriers of the multiplex and τ0 denotes the temporal spacing between two real-value symbols, the following are transmitted for a same inter-carrier spacing ν0:                in OFDM/OQAM, one real value per carrier at every time slot τ0;        in classic OFDM without guard interval, one complex value (i.e. two real values) every 2×τ0=Tu.        
In other words, the spectral efficiency of OFDM/OQAM is (Tg+2τ0)/2τ0 times greater than that of classic OFDM with a guard interval of a duration Tg.
1.3 BFDM/OQAM Modulation
Furthermore, if we choose to have demodulation functions on the reception side that are not necessarily the conjugate functions of the prototype functions used in transmission, it is possible by using the property of biorthogonality, to generalize OFDM/OQAM to the BFDM/OQAM modulation technique.
The offset principle, related to the OQAM family is strictly identical in the context of a BFDM/OQAM type modulation. Consequently, FIG. 1 can also be applied to BFDM/OQAM type modulations.
More specifically, the value of BFDM/OQAM type modulation is that, for a given length of prototype filter, it enables a reduction in the delay due to the transmission system.
As indicated here above, the BFDM/OQAM modulation technique, just like the OFDM/OQAM modulation technique, transmits real-valued symbols at a rate that is twice the rate at which the OFDM transmits complex-value symbols. Consequently, these two modulations have in principle the same spectral efficiency.
More specifically, the BFDM/OQAM signal can be represented in baseband in the following form:
                                          s            ⁡                          (              t              )                                =                                    ∑              n                        ⁢                                          ∑                                  m                  =                  0                                                  M                  -                  1                                            ⁢                                                a                                      m                    ,                    n                                                  ⁢                                                      g                    ⁢                                          (                                              t                        -                                                  n                          ⁢                                                                                                          ⁢                                                      τ                            0                                                                                              )                                        ⁢                                          ⅇ                                              j                        ⁢                                                                                                  ⁢                        2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                        m                        ⁢                                                                                                  ⁢                                                  v                          0                                                ⁢                        t                                                              ⁢                                          ⅇ                                              j                        ⁢                                                                                                  ⁢                                                  ϕ                                                      m                            ,                            n                                                                                                                                                    ︸                                                                  g                                                  m                          ,                          n                                                                    ⁡                                              (                        t                        )                                                                                                                                ,                            (        1        )            
with:                am,n the real data elements to be transmitted on a carrier m at the instant n;        M the number of carrier frequencies (necessarily an even number);        g the prototype function used by the modulator;        τ0 the duration of a BFDM/OQAM symbol;        ν0 the inter-carrier spacing;        φm,n is a phase term chosen so as to obtain a real part/imaginary part alternation enabling the orthogonality or more generally biorthogonality to be obtained.        
Indeed, in the biorthogonal case, the demodulation base at reception may be different from that of transmission, and can be expressed in the following form:fm,n(t)=f(t−nτ0)ej2πmν0tejφm,n  (2)
The condition of biorthogonality can then be expressed in the following form:
                                          〈                                          g                                  m                  ,                  n                                            ,                              f                                                      m                    ′                                    ,                                      n                    ′                                                                        〉                    R                =                              ℜ            ⁢                          {                                                ∫                                      -                    ∞                                    ∞                                ⁢                                                                            g                                              m                        ,                        n                                                              ⁡                                          (                      t                      )                                                        ⁢                                                            f                                                                        m                          ′                                                ,                                                  n                          ′                                                                    *                                        ⁡                                          (                      t                      )                                                        ⁢                                      ⅆ                    t                                                              }                                =                                    δ                              m                ,                                  m                  ′                                                      ⁢                          δ                              n                ,                                  n                  ′                                                                                        (        3        )            where: .,.R designates the real scalar product and { } designates the real part.
However, one drawback of BFDM/OQAM (or OFDM/OQAM) type modulation techniques is that the condition of biorthogonality (or orthogonality) is obtained only for real values of symbols to be transmitted. This raises a problem of estimation at reception, and especially of estimation of the transmission channel, in as much as the symbols received are complex symbols.
2. The Transmission Channel
Here below, a brief description is given of the characteristics of a transmission channel, especially in a radiomobile environment, and of the techniques of estimation of such a channel. It may be recalled indeed that the method for shaping an electrical signal from the information to be transmitted depends on the conditions in which such a signal is transmitted.
2.1 Characteristics of the Transmission Channel
In a radiomobile environment, the transmitted wave, in its journey, undergoes numerous reflections and the receiver therefore receives a sum of delayed versions of the sent signal. Each of these versions is attenuated and phase shifted randomly. This phenomenon known as “delay spread” generates inter-symbol interference (ISI). The term ISI is understood to mean especially interference between temporal symbols and/or between carriers. For example, in an urban type of environment, the delay spread is in the range of some microseconds or less.
Since the receiver (for example a motorist's mobile radio telephone) is assumed to be moving, the effect known as the Doppler effect also acts on each path, resulting in a shift in the frequency of the received spectrum that is proportional to the speed of movement of the mobile.
The combined action of these effects is expressed in the form of a non-stationary channel having profound fading effects at certain frequencies. A channel of this kind is qualified especially as a frequency-selective channel. In certain applications, which are particularly worthwhile in the context of the present invention, the transmission band has a width greater than that of the coherent band of the channel (i.e. the band for which the frequency response of the channel may be considered to be constant over a given period of time). Fading phenomena therefore appear in the band, i.e. at a given point in time, certain frequencies are highly attenuated.
To overcome these different phenomena (due to the ISI and to the Doppler effect), it has been envisaged in OFDM type systems to add a guard interval during which no payload information is transmitted so as to ensure that all the pieces of information received come from a same symbol. In the case of a consistent demodulation of sub-carriers, the distortion given by the channel is then corrected by estimating its value at every point of the time/frequency network.
The introduction of a guard interval of this kind thus reduces the phenomena related to inter-symbol interference.
However, one major drawback of this technique is that its spectral efficiency is limited since no payload information is transmitted during the guard interval.
On the other hand, OFDM/OQAM and BFDM/OQAM type modulation techniques do not necessitate the introduction of a guard interval or a cyclic prefix, while at the same time having the same spectral efficiency as classic OFDM modulation.
2.2 Estimation of the Transmission Channel
The distinct features of real type multicarrier modulations on the one hand and complex type multicarrier modulations on the other hand give rise to different types of processing when an estimation of the transmission channel is performed.
In the OFDM/OQAM context, a method has been envisaged in particular relying on the implementation of an estimation by reference symbols. In this technique, at least one reference symbol is placed at the start of a frame, a frame being constituted by a set of at least one reference symbol, called a preamble, and a set of payload symbols. Using these symbols or this symbol, the channel is estimated on each of the carriers of the multiplex. The choice of the parameters of the system (symbol duration, frame length etc) ensures that the channel will vary slowly relative to the symbol time. It is then assumed to be quasi-constant on a frame. It is possible therefore to choose the estimate of the channel on the reference symbols for all the OFDM symbols of the frame.
Indeed, to estimate the complex gain of the channel on a given sub-carrier, it would be appropriate to carry out the complex projection of the received signal on the sub-carrier considered. Now, the orthogonality of the translated values in the real sense and the fact that the prototype functions, even those chosen to be localized to the utmost extent in time and in frequency, have an infinite support on at least one of the two axes namely the time axis or the frequency axis, implying that even on an ideal channel, (intrinsic) inter-carrier interference will be generated.
Indeed, the imaginary part of the projection of the signal received on the base of the translated values of the prototype function is not 0. A disturbance-causing term then appears and gets added to the demodulated signal, and has to be corrected before the channel estimation is done. It is therefore necessary to design methods to compensate for this loss of complex orthogonality and thus mitigate at least some of the drawbacks of this prior-art technique for OFDM/OQAM or BFDM/OQAM type modulations.
Let us consider for example y(t) the signal received.
It is assumed especially that the choice of the parameters of the multicarrier modulation ensures that the channel may be considered to be flat on each of the sub-carriers for each OFDM/OQAM symbol. The channel can then be modeled by one complex coefficient per sub-carrier denoted Hm,n, where m is the index of the sub-carrier and n is the index of the OFDM/OQAM symbol.
We then use the complex projection of the multicarrier signal at the point (m0, n0) of the time/frequency space to estimate the transmission channel Ĥm0,n0 at this location.
Thus, if we send am0,n0=√{square root over (E)} at this location, we have:
                                          H            ^                                              m              0                        ,                          n              0                                      =                              ∫                                          y                ⁡                                  (                  t                  )                                            ⁢                                                g                                                            m                      0                                        ,                                          n                      0                                                        *                                ⁡                                  (                  t                  )                                            ⁢                              ⅆ                t                                                          E                                              (        4        )            
Assuming that the channel is ideal (y(t)=s(t)), given that the OFDM/OQAM and BFDM/OQAM modulations have only real orthogonality (equation (3)), we cannot have Ĥm0,n0=1.
Therefore, taking am0,n0(c)=s,gm0,n0C=∫s(t)gm0,n0(t)dt, and assuming that the channel is ideal, we have:
                              a                                    m              0                        ,                          n              0                                            (            c            )                          =                              E                    +                                                    ∑                                                      (                                          m                      ,                      n                                        )                                    ≠                                      (                                                                  m                        0                                            ,                                              n                        0                                                              )                                                              ⁢                                                a                                      m                    ,                    n                                                  ⁢                                  ∫                                                                                    g                                                  m                          ,                          n                                                                    ⁡                                              (                        t                        )                                                              ⁢                                                                  g                                                                              m                            0                                                    ,                                                      n                            0                                                                          *                                            ⁡                                              (                        t                        )                                                              ⁢                                          ⅆ                      t                                                                                                          ︸                                                I                                                            m                      0                                        ,                                          n                      0                                                                      ∈                                  j                  ⁢                                                                          ⁢                  ℜ                                                                                        (        5        )            
where ,.C designates the complex scalar product.
The equation (5) expresses the fact that the complex projection of the perfectly transmitted signal is nevertheless affected by an inter-symbol interference (ISI) intrinsic to the OFDM/OQAM and BFDM/OQAM modulations denoted as Im0,n0.
In particular, the existence of this inter-symbol interference greatly disturbs the estimation of the transmission channel and therefore the estimation of the symbols.
One solution to this problem has been proposed especially in the patent document WO 02/25884 published on 28 Mar. 2002 in the context of a channel estimation by reference symbols for a multicarrier signal comprising at least one frame.
More specifically, the technique proposed in this document enables this interference to be limited by using a specific framing of the data at sending, relying on the insertion of a preamble. Thus, the intrinsic interference affecting the reference symbols of the frames of the multicarrier signal is reduced by dictating a constraint on the value of at least one of the data elements of the reference symbols.
Thus, this technique associates a reference data element called a pilot as well as a piece of control data with 3×3 zones of the time/frequency network, called first-ring zones or greater-sized zones.
However, one drawback of this technique relying on the insertion of the preamble is the loss of spectral efficiency related to the sending of the preamble, this preamble being classically formed by at least three reference symbols, during which no payload information is transmitted.
Another drawback of this prior-art technique is that the sequences used to reduce the intrinsic interference have a periodic character leading to a very high variation in the dynamic range of the multicarrier signal, and for example in the power average peak ratio (PAPR) on the preambles.
Furthermore, this technique is limited to certain types of prototype filters and/or types of modulations.
Another drawback of this prior-art technique is that it calls for a matrix computation at sending and at reception, with a matrix size that increases with the size of the ring.
There is therefore a need for a technique providing for a better estimation of the transmission channel and giving a more precise estimation of the informative data elements carried by the multicarrier signal.